20.309:Measuring DNA Melting Curves

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(Model vs. reality)
(Model vs. reality)
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</math>.
</math>.
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Here, <math>f</math> is the fraction of DNA strands hybridized (dimerized) at a particular temperature (at <math>T_m</math>, this is 1/2), and <math>C_T</math> is the total concentration of single-strand oligonucleotides (or 2X the dsDNA concentration when all strands are hybridized). Choose one of the perfect-match sequences that you measured, and use matlab to fit the model to your measured data, which will allow you to extract the <math>\Delta H^{\circ}</math> and <math>\Delta S^{\circ}</math> parameters. To perform the fit, you will need a matlab function that will evaluate T(f) given an input const for the ¢Hff and ¢Sff parameters. The function will be something like this:  
+
Here, <math>f</math> is the fraction of DNA strands hybridized (dimerized) at a particular temperature (at <math>T_m</math>, this is 1/2), and <math>C_T</math> is the total concentration of single-strand oligonucleotides (or 2X the dsDNA concentration when all strands are hybridized). Choose one of the perfect-match sequences that you measured, and use matlab to fit the model to your measured data, which will allow you to extract the <math>\Delta H^{\circ}</math> and <math>\Delta S^{\circ}</math> parameters. To perform the fit, you will need a matlab function that will evaluate <math>T(f)</math> given an input <font face="Courier">const</font> for the <math>\Delta H^{\circ}</math> and <math>\Delta S^{\circ}</math> parameters. The function will be something like this:  
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You can then invoke matlab's 'lsqcurvefit' routine to do the fit, which will return the best values for <math>\Delta H^{\circ}</math> and <math>\Delta S^{\circ}</math>.  
+
You can then invoke matlab's <font face="Courier">lsqcurvefit</font> routine to do the fit, which will return the best values for <math>\Delta H^{\circ}</math> and <math>\Delta S^{\circ}</math>.  
<pre>
<pre>

Revision as of 13:47, 5 September 2007

This is a work in progress. Please check back for the final version.

DNA Melting Apparatus
DNA Melting Apparatus

Contents

Introduction

In this lab, you will measure the melting temperature of several DNA samples to determine the effect of sequence length, ionic strength and complementarity. A common application of this technique exploits the length dependence of DNA melting temperatures to examine PCR products in order to determine whether a desired sequence was successfully amplified.

The measurement technique utilizes a fluorescent dye that binds preferentially to double stranded DNA (dsDNA). This characteristic of the dye allows the relative concentration of dsDNA to be determined by measuring the intensity of fluorescent light given off by an excited sample.

The DNA melting apparatus you will construct consists of four major subsystems: excitation, fluorescence measurement, temperature sensing, and data acquisition. You will build these subsystems out of an LED, a photodiode, a resistance temperature detector (RTD), and a PC data acquisition system.

The goal of your time in the lab will be to measure fluorescence intensity versus temperature for each of the samples over a range of about 90°C to room temperature. This will provide a basis for estimating the melting temperature, Tm of each sample. (Tm is defined as the temperature where half of the DNA in the sample remains hybridized.)

Three of the samples will be unknown. All the unknowns will have the same length, but different degrees of complementarity: complete match, single mismatch, and complete mismatch. Using the data you gather, you will attempt to identify these three samples.

Overview of the apparatus

In most DNA melting apparatuses, the temperature of the sample is ramped up at a controlled rate and the concentration of dsDNA recorded. In our homebrew setup, however, we will first heat up the sample on a hot plate. That way, natural cooling will provide the range of temperature conditions needed. As the sample cools, a PC data acquisition card will record the photodiode and RTD outputs over time. During data analysis, you will convert these voltages to temperature and relative dsDNA concentration. The melting temperature, Tm can be estimated from a graph of this data or its derivative.

When bound to dsDNA, SYBR Green I is most sensitive to blue light with a wavelength of 498 nm. The dye emits green light with a wavelength of 522 nm. You can easily observe this – a room-temperature sample of dsDNA and SYBR green looks yellow from the combination of blue excitation and green fluorescence. At higher temperatures, when there is no dsDNA to bind to, the sample will appear blue or clear.

In addition to dsDNA concentration, SYBR Green's fluorescence intensity dependens on temperature. Higher temperatures reduce its fluorescence. This introduces an approximately linear error term into the signal as the temperature is ramped. The temperature dependence of SYBR Green can be accounted for in a variety of ways during analysis, including taking the derivative of the data.

As shown in the diagram, an aluminum heating block holds a cuvette containing the sample under test. The sample is a combination of DNA and a fluorescent dye called SYBR Green. In addition to being a convenient holder, the block gives the setup enough thermal inertia to facilitate a measurement from natural cooling. (Without the block, the sample would cool too quickly.)

Blue light from an LED illuminates one side of the cuvette. An optical filter shapes the output of the LED so that only the desired spectral range falls on the sample.

In the DNA melting apparatus, a photodiode placed at 90 degrees to the LED source detects the green light emitted by bound SYBR Green. The photodiode is placed behind an optical filter to ensure that only the fluorescent light given off by the sample is detected.

Since photodiodes produce only a very small amount of current, it will be necessary to build a very high gain transimpedence amplifier to produce a signal that is measurable by the PC data acquisition cards. Photodiode amplifiers are particularly challenging because many of the non-ideal characteristics of op amps become apparent at high gain.

An RTD attached to the heating block and wired to a voltage divider provides an indication of temperature. The temperature of the heating block will be a proxy for the sample temperature. Unfortunately, the block cools faster when it is hot than when it is near room temperature. You will have to get the heating block set up in your apparatus quickly after you remove it from the heating block.

The amplified photodiode output and the voltage across the RTD will be connected to two channels of the CP data acquisition card. A virtual instrument (called a VI) written in LabView will record the RTD and diode outputs. The DNA melting VI has a button to save data in file that can be loaded into Matlab for analysis.

Objectives and learning goals

  • Measure temperature with an RTD.
  • Implement a high gain transimpedence amplifier for photodiode current multiplication.
  • Measure light intensity with a photodiode.
  • Build an optical system for exciting the sample with blue light and gathering the fluorescence output on the photodiode.
  • Record dsDNA concentration versus temperature curves for several samples.
  • Estimate Tm from your data.
  • Compare the measured DNA melting with theoretical models.
  • Identify unknown DNA samples.

Lab procedure

Roadmap

  1. Build an optical system containing the LED, heating block, sample, photodiode, filters, and lenses.
  2. Hook up a three terminal voltage regulator to create an electrical power supply for the LED.
  3. Build, test, and calibrate the temperature-sensing circuit.
  4. Build an amplification/offset circuit for the DNA fluorescence signal.
  5. Troubleshoot and optimize your system.
  6. Heat a samples of DNA with SYBR Green dye and record DNA melting curves as the samples cool.
  7. Analyze the data. Identify the three unknown samples. Compare your observations to theoretical models.

Optical system

TODO: Add figure with diagram of setup. TODO: Add picture of example setup.

The optical system consists of an LED, excitation filter, sample cuvette, heating block, emission filter, photodiode, optional lenses, and associated mounting hardware. Construct your system on an optical breadboard. The breadboard has a grid of tapped holes for mounting all kinds of optical and mechanical hardware. ThorLabs manufactures most of the hardware stocked in the lab. A few of the components you will certainly use include: 1/2" diameter posts, CP02 cage plates, and 1” diameter lens tubes.

Use optical rails and rail carriers or optical bases to mount 1/2” posts on the breadboard. RA90 right angle post clamps and post holderscan also be useful.

There are a variety of ways to construct your apparatus. A good design will be compact, stable, and simple. You will have to shield the optical system from ambient light, so a small footprint will be advantageous.

Illumination

Begin by mounting the LED on your breadboard. Note that there are two styles of LEDs. The Lamina LED Array is mounted on an aluminum heat sink and bolted to a CP02 cage plate. The CP02 attaches to the top of a post. It has an SM1 threaded hole through the middle that connects to 1” diameter lens tubes. The Cree LEDs are already mounted in a 1” lens tube.

Both styles of LED emit a range of wavelengths with a peak at 475 nm. A Chroma Technology D470 filter eliminates unwanted parts of the spectrum that might interfere with detection of the fluorescence signal. The filters have exposed, delicate coatings and must be handled carefully. In addition, the filter works better in one direction than the other.

Light from both kinds of LEDs diverges in a cone with an angle of about 100 degrees, so place the device close to the sample. You can also use a lens to concentrate the LED's output. Several lenses are available in the lab:

Fluorescence detection

The SM05PD1A photodiode is mounted in a short tube with SM05 threads. Use a SM1A6 adapter to mount the photodiode in a CP02 cage plate. Mount the photodiode assembly to the breadboard at 90 degrees to the LED. Build a system to hold the emission filter in front of the photodiode. You can use a lens to focus light from the sample on to the detector to improve performance, if you like.

Put an optical quick connect at the end of the photodiode assembly to facilitate easy attachment of the heating block during experimental runs. The other half of the quick connect goes into the CP02 cage plate mounted on the heating block.

Electrical System

Temperature

The electrical resistance of most materials varies with temperature. An RTD is a special resistor (usually made out of platinum) that exhibits a nearly linear change in its value with temperature. An RTD may be used to accurately measure temperature by including it as an element in a voltage divider. As the resistance of the RTD changes, so will the voltage across it.

A PPG102A1 RTD has been pre-mounted to the DNA heating block. This RTD has a nominal resistance of 1 KΩ and its value increses with temperature. Note that the maximum current carrying capacity of this device is 1 ma. Hook up the RTD in a voltage divider. Make sure the divider has no more than 1 mA flowing through it. Use freeze spray or heat the block on the warmer to test the circuit.

Fluorescence intensity

Amplification circuit

Schematic diagram of a high gain transimpedence amplifier.
Schematic diagram of a high gain transimpedence amplifier.

The photodiode produces only a tiny current – on the order of nanoamps. Its output must be amplified and converted to a voltage measurable by the PC data acquisition system. A transimpedance amplifier (sometimes called a current-to-voltage converter) with a gain of approximately 108 V/A will be required. The circuit considered in Homework 1 is capable of providing this gain. (Optional question: why not simply use a resistor, and omit the op-amp?)

Photodiode amplifiers can be fiddly under the best of circumstances. At such high gain, many of the non-ideal behaviors of op amps become apparent. It will be important to keep your wiring short and neat. The amplifier and witing will also be susceptible to physical movement, so prevent things from getting bumped during experimental runs. In addition select an op amp that has a very low input bias current as possible. (Why?) Op amps with JFET inputs like the LF411 and LF351 generally have the lowest input current.

TODO: add noise from cable shield, ground strapping, capacitor

Offset circuit

Figure 5: Offset circuit using the LM741. Note that all three of the pot's leads are used, and the wiper is connected to the negative sup- ply voltage.

A final addition to the system that will greatly improve its usabil- ity is a knob that lets you control the level of the output signal. A simple way to do this is using an LM741 op-amp, with a 10k­ potentiometer connected as shown in Fig. 5. Use one of the high- quality round pots to obtain smooth and precise control.

TODO: Figure 6: Recommended layout of the light source, filters, and detector for the optics setup.

Optical system

The LED array connects to the circuit just like a single LED, using two leads - anode and cathode. It can be powered directly from your power supply, and ¼ 8:8V is known to supply a good amount of light while dissipating manageable heat.

TODO: Add info about voltage regulator an ned LEDs

PC Data Acquisition System

TODO: describe the DAQ system and capabilities.

LabVIEW VI

TODO: instructions for operating the VI

Debugging the apparatus

  1. Do this first without the sample and the block. Using a box and a piece of black cloth, make sure the entire optical setup is isolated from stray light. If you can see any blue light coming out at all, light is also getting in.
  2. Use the potentiometer to adjust the amplifier voltage offset until the baseline signal is approx. 0 V.
  3. The baseline should be relatively flat { if it is not, generally it's because the setup is not well covered.
  4. Now include the block with DNA solution in the setup. Adjust the block's placement and the angle of the LED source to maximize the ratio of DNA signal vs. background signal without

TODO: measure water vs sample

Experimental procedure

Once your instrument is running to your satisfaction, measure melting curves each of the 5 conditions:

  • 40bp perfect match
  • 3 unknown 20 bp sequences (perfect match, single mismatch, and complete mismatch)
  • 20 bp perfect match at different ionic strength

If you have time, you can run additional experiments. For example, you could gather additional ionic strength data points.

The DNA melting apparatus will generate the best data when both the amplifier circuit and LED have been on for a while and all the components have reached their steady state temperature. Make sure the outupts of the system are stable before you begin taking data. Turn your apparatus on and measure the difference between a cool DNA sample and water. Run the DNA melting LabVIEW VI in the DNAMelting directory of the course locker. Adjust the range controls for each channel to provide the greatest measurement resolution.

The steps for each experimental run are:

  1. Heat up the sample on the hot plate
  2. Quickly transfer the sample to your setup
  3. Cover the apparatus to block out ambient light
  4. Start recording RTD and photodiode output with the LabVIEW VI.
  5. Wait for the block to cool to below 40°C

Prepare a sample

Pipet 500μl of DNA plus dye solution into a disposable plastic cuvette. Pipet 20μl of mineral oil on top of the sample to help prevent evaporation. Put a top on the cuvette and mark it with a permanent marker. Keep the sample vertical to make sure the oil stays on top. You should be able to use the same sample for many heating/cooling cycles. Only discard it if you lose significant volume due to evaporation. If you need to leave the sample overnight, store it in the lab refrigerator. If you finish with a sample and it is still in good shape, pass it on to another group.

Heat up the sample

Place your heating block and sample on the hot plate (set to about 95° C). You can use a DVM to monitor the temperature of the holder. It takes longer than you think -- more than 10 minutes. Heat up the block to a temperature above where the DNA melts (at least 80° C) and then transfer the block to your setup. Hook up the RTD and record the cooling curve using the LabView DNA Melting VI.

Report Requirements

Data Analysis

(Note: Other than the last one, the 19bp samples will only be identified as A, B, and C, and you will need to identify, based on your measurements, which is which.) You will need to take the derivative of the recorded fluorescence data, and combine it with the temperature data to generate plots. Generally, the region of interest will fall between 40 and 65ffC. It will be helpful to create a matlab script to convert raw data to a plot of dF/dT vs. temperature.

When you plot your data in Matlab, you may notice it looks discontinuous or noisy. You may process the data how you wish, however a useful command in Matlab is resample . This function can not only resample data, as the name implies, but will also apply a low-pass filter (decreasing the high-frequency noise). A larger vector of filter coefficients or number of samples on each side of the current sample will smooth the data more. Using this command, pay attention to the resulting length of your new data, as well as any inaccuracies at the ends (what does resample assume for the data points before and after your data?). Derivatives may require filtering as well.

he \melting temperature" Tm is defined as the temperature at which 50% of the DNA remains hybridized. Sometimes, the transition is not particularly sharp, or other factors in the measurement may create offsets or drifts in the signal (evident below 80±C in Fig.1(a)), in which case the derivative of this curve is plotted (Fig. 1(b)), and the location of its peak value gives Tm more clearly. More about this in Section 4.2.3.

Having generated your melting profiles, you need to produce the following plots:

  1. Comparison of perfect match 40bp and 19bp sequences.
  2. Comparison of 19bp perfect match vs. SNP vs. complete mismatch sequences.
  3. Comparison of 19bp sequences at different ionic strengths.

In each situation, discuss the melting temperatures and shapes of the melting curves for the samples relative to each other. Briefly explain the curves are the way they are in each case. Compare your melting curves with those of other students in the class. You may find the quite different even under the same conditions. What might cause these variations? What factors affect the DNA melting temperature, and the \sharpness" of the melting transition?

Model vs. reality

In class, we derived an expression that relates the melting temperature to the enthalpy change \Delta H^{\circ} and entropy change \Delta S^{\circ} of the hybridization reaction:


T(f) = \frac{\Delta H^{\circ}}{\Delta S^{\circ}-R \ln
(2f/C_T(1-f)^2)}
.

Here, f is the fraction of DNA strands hybridized (dimerized) at a particular temperature (at Tm, this is 1/2), and CT is the total concentration of single-strand oligonucleotides (or 2X the dsDNA concentration when all strands are hybridized). Choose one of the perfect-match sequences that you measured, and use matlab to fit the model to your measured data, which will allow you to extract the \Delta H^{\circ} and \Delta S^{\circ} parameters. To perform the fit, you will need a matlab function that will evaluate T(f) given an input const for the \Delta H^{\circ} and \Delta S^{\circ} parameters. The function will be something like this:

function Tf = melt(const, f) 
R=8.3; 
C_T=33e-6; 
dH = const(1); 
dS = const(2); 
Tf = dH./(dS - R*log(2*f./(C_T*(1-f).^2))); 

You can then invoke matlab's lsqcurvefit routine to do the fit, which will return the best values for \Delta H^{\circ} and \Delta S^{\circ}.

FitVals = lsqcurvefit(@melt, [dH_guess, dS_guess], frac_vector, temp_vector) 

Bonus (optional):

1. Calculate \Delta H^{\circ} and \Delta S^{\circ} for this sequence using the nearest-neighbor model from class.

2. Compare these to the fit parameters, and speculate about why they might be different? What factors affect \Delta H^{\circ} and \Delta S^{\circ}?

External references

TODO: Bypass caps, grounding, don’t let diode shield touch ground

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